Since both centers are on the red line y = x,
we can let the smaller circle have radius r and center A(r,r)
and let the larger circle have radius R and center B(R,R) 

We want to find the difference between between R and r,

so we want to find R-r.

We use the distance formula to find the distance between
the centers A(r,r) and B(R,R)

d =   

where (x1,y1) = (r,r)
and where (x2,y2) = (R,R)

We are given that the distance between centers is 8.  
So we have

 = 8
 = 8
 = 8

Divide both sides by 

R-r =  
R-r = 
R-r = 

Edwin